Can I get an example (and a small slice of work) of multiplying radical expressions?

That is cute - and very derpy.   :)     (AND EFFECTIVE - I am not criticizing)

$$6\sqrt[5]{32m^3}\times5\sqrt[5]{1024m^2}\\\\
=6*5\sqrt[5]{32*1024m^3m^2}\\\\
=6\sqrt[5]{32*1024m^5}\\\\
=6\sqrt[5]{32*1024}\;\sqrt[5]{m^5}\\\\
=6\sqrt[5]{32*1024}\;\sqrt[5]{m^5}\\\\
=6\sqrt[5]{32*1024}\;m\\\\$$

$${\sqrt[{{\mathtt{{\mathtt{5}}}}}]{\left({\mathtt{32}}{\mathtt{\,\times\,}}{\mathtt{1\,024}}\right)}} = {\mathtt{8}}$$

$$\\=6\sqrt[5]{32*1024}\;m\\\\
=6*8\;m\\\\
=48m$$

Does that help?

It would also be very useful for you to know that fifth root is the same as a power of 1/5

$$\sqrt[5]{32}=32^{1/5}$$

If you are going to put this into any calc it could be done as

32^(1/5)=

In the web2 calc you could also type in sqrt(32,5) and press the equals.  This is just another way to do it.

Maybe you should give us an example of your homework so that we can gauge the difficulty level.

A little derpy, not going to lie, but:

I couldnt figure out how to put the exponents in the square like that, so I just drew them on 

Yes, thank you ^_^